IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v176y2023ics0960077923010536.html
   My bibliography  Save this article

Hysteresis and Hopf bifurcation: Deciphering the dynamics of an in-host model of SARS-CoV-2 with logistic target cell growth and sigmoidal immune response

Author

Listed:
  • Kumawat, Nitesh
  • Rashid, Mubasher
  • Srivastava, Akriti
  • Tripathi, Jai Prakash

Abstract

Mathematical models of in-host dynamics of SARS-CoV-2 may reveal the intricate underlying dynamics of host-pathogen interaction and guide crucial steps to curtail progression of COVID-19 and other similar infectious diseases. While the existing models on SARS-CoV-2 have considered a wide range of host-pathogen interactions, at their core, these models are remarkably similar, particularly in the choice of mathematical functions used in modeling the interactions. Specifically, these models have employed mass action kinetics while modeling target-cell interaction with virus particles and immune response to virus, thus overlooking the role of saturated evolution of target epithelial cells as well as immune cells. Here we fill this gap by developing a more comprehensive model of in-host dynamics of SARS-CoV-2 that concurrently models target epithelial cell growth using a logistic equation and virus-immune interaction using Michaelis–Menten kinetics. We identify a feasible disease-free equilibrium whose local stability depends on ”reproduction number” and global stability on the replenishment rate as well as the removal rate of immune cells. We also obtain multiple endemic equilibria and perform their local and global stability analysis. Our detailed numerical investigation demonstrates that the infection rate and reproduction number govern several interesting dynamical behaviors such as forward bifurcation with and without hysteresis, Hopf bifurcation, and multiple endemic equilibria. To analyze the impact of parameters on the model system and disease dynamics, we investigate several sensitive parameters and compute their sensitivity indices. Finally, to understand the impact of anti-viral therapy on viral load, we identify a novel threshold of replication rate that must be crossed to enable virus proliferation. Our results thus provide novel insights into the in-host dynamics of SARS-CoV-2 and we expect this model will help in the development of better treatment strategies for COVID-19 and other such infectious diseases.

Suggested Citation

  • Kumawat, Nitesh & Rashid, Mubasher & Srivastava, Akriti & Tripathi, Jai Prakash, 2023. "Hysteresis and Hopf bifurcation: Deciphering the dynamics of an in-host model of SARS-CoV-2 with logistic target cell growth and sigmoidal immune response," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010536
    DOI: 10.1016/j.chaos.2023.114151
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923010536
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114151?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Roman Wölfel & Victor M. Corman & Wolfgang Guggemos & Michael Seilmaier & Sabine Zange & Marcel A. Müller & Daniela Niemeyer & Terry C. Jones & Patrick Vollmar & Camilla Rothe & Michael Hoelscher & To, 2020. "Author Correction: Virological assessment of hospitalized patients with COVID-2019," Nature, Nature, vol. 588(7839), pages 35-35, December.
    2. Benlloch, José-María & Cortés, Juan-Carlos & Martínez-Rodríguez, David & Julián, Raul-S. & Villanueva, Rafael-J., 2020. "Effect of the early use of antivirals on the COVID-19 pandemic. A computational network modeling approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Y. Fadaei & F. A. Rihan & C. Rajivganthi & Ning Cai, 2022. "Immunokinetic Model for COVID-19 Patients," Complexity, Hindawi, vol. 2022, pages 1-13, June.
    4. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "Mathematical Modeling of Immune Responses against SARS-CoV-2 Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(19), pages 1-13, September.
    5. Roman Wölfel & Victor M. Corman & Wolfgang Guggemos & Michael Seilmaier & Sabine Zange & Marcel A. Müller & Daniela Niemeyer & Terry C. Jones & Patrick Vollmar & Camilla Rothe & Michael Hoelscher & To, 2020. "Virological assessment of hospitalized patients with COVID-2019," Nature, Nature, vol. 581(7809), pages 465-469, May.
    6. Juan Carlos Chimal-Eguia, 2021. "Mathematical Model of Antiviral Immune Response against the COVID-19 Virus," Mathematics, MDPI, vol. 9(12), pages 1-19, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tobias Schlager & Ashley V. Whillans, 2022. "People underestimate the probability of contracting the coronavirus from friends," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-11, December.
    2. Joseph Pateras & Preetam Ghosh, 2022. "A Computational Framework for Exploring SARS-CoV-2 Pharmacodynamic Dose and Timing Regimes," Mathematics, MDPI, vol. 10(20), pages 1-12, October.
    3. Marta Baselga & Juan J. Alba & Alberto J. Schuhmacher, 2022. "The Control of Metabolic CO 2 in Public Transport as a Strategy to Reduce the Transmission of Respiratory Infectious Diseases," IJERPH, MDPI, vol. 19(11), pages 1-19, May.
    4. Lisa Cariani & Beatrice Silvia Orena & Federico Ambrogi & Simone Gambazza & Anna Maraschini & Antonella Dodaro & Massimo Oggioni & Annarosa Orlandi & Alessia Pirrone & Sara Uceda Renteria & Mara Berna, 2020. "Time Length of Negativization and Cycle Threshold Values in 182 Healthcare Workers with Covid-19 in Milan, Italy: An Observational Cohort Study," IJERPH, MDPI, vol. 17(15), pages 1-10, July.
    5. Dapeng Li & David R. Martinez & Alexandra Schäfer & Haiyan Chen & Maggie Barr & Laura L. Sutherland & Esther Lee & Robert Parks & Dieter Mielke & Whitney Edwards & Amanda Newman & Kevin W. Bock & Mahn, 2022. "Breadth of SARS-CoV-2 neutralization and protection induced by a nanoparticle vaccine," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    6. Susanna Esposito & Federico Marchetti & Marcello Lanari & Fabio Caramelli & Alessandro De Fanti & Gianluca Vergine & Lorenzo Iughetti & Martina Fornaro & Agnese Suppiej & Stefano Zona & Andrea Pession, 2021. "COVID-19 Management in the Pediatric Age: Consensus Document of the COVID-19 Working Group in Paediatrics of the Emilia-Romagna Region (RE-CO-Ped), Italy," IJERPH, MDPI, vol. 18(8), pages 1-29, April.
    7. Ramon Roozendaal & Laura Solforosi & Daniel J. Stieh & Jan Serroyen & Roel Straetemans & Anna Dari & Muriel Boulton & Frank Wegmann & Sietske K. Rosendahl Huber & Joan E. M. van der Lubbe & Jenny Hend, 2021. "SARS-CoV-2 binding and neutralizing antibody levels after Ad26.COV2.S vaccination predict durable protection in rhesus macaques," Nature Communications, Nature, vol. 12(1), pages 1-10, December.
    8. Shengwei Zhu & Tong Lin & John D. Spengler & Jose Guillermo Cedeño Laurent & Jelena Srebric, 2022. "The Influence of Plastic Barriers on Aerosol Infection Risk during Airport Security Checks," Sustainability, MDPI, vol. 14(18), pages 1-14, September.
    9. Sasha Harris-Lovett & Kara L. Nelson & Paloma Beamer & Heather N. Bischel & Aaron Bivins & Andrea Bruder & Caitlyn Butler & Todd D. Camenisch & Susan K. De Long & Smruthi Karthikeyan & David A. Larsen, 2021. "Wastewater Surveillance for SARS-CoV-2 on College Campuses: Initial Efforts, Lessons Learned, and Research Needs," IJERPH, MDPI, vol. 18(9), pages 1-20, April.
    10. Maria de Lourdes Aguiar-Oliveira & Aline Campos & Aline R. Matos & Caroline Rigotto & Adriana Sotero-Martins & Paulo F. P. Teixeira & Marilda M. Siqueira, 2020. "Wastewater-Based Epidemiology (WBE) and Viral Detection in Polluted Surface Water: A Valuable Tool for COVID-19 Surveillance—A Brief Review," IJERPH, MDPI, vol. 17(24), pages 1-19, December.
    11. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "Mathematical Modeling of Immune Responses against SARS-CoV-2 Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(19), pages 1-13, September.
    12. Jaclyn A. Kaiser & Christine E. Nelson & Xueqiao Liu & Hong-Su Park & Yumiko Matsuoka & Cindy Luongo & Celia Santos & Laura R. H. Ahlers & Richard Herbert & Ian N. Moore & Temeri Wilder-Kofie & Rashid, 2024. "Mucosal prime-boost immunization with live murine pneumonia virus-vectored SARS-CoV-2 vaccine is protective in macaques," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    13. Chih-Chia Hsieh & Chih-Hao Lin & William Yu Chung Wang & David J. Pauleen & Jengchung Victor Chen, 2020. "The Outcome and Implications of Public Precautionary Measures in Taiwan–Declining Respiratory Disease Cases in the COVID-19 Pandemic," IJERPH, MDPI, vol. 17(13), pages 1-10, July.
    14. Abdin, Adam F. & Fang, Yi-Ping & Caunhye, Aakil & Alem, Douglas & Barros, Anne & Zio, Enrico, 2023. "An optimization model for planning testing and control strategies to limit the spread of a pandemic – The case of COVID-19," European Journal of Operational Research, Elsevier, vol. 304(1), pages 308-324.
    15. Jos Lelieveld & Frank Helleis & Stephan Borrmann & Yafang Cheng & Frank Drewnick & Gerald Haug & Thomas Klimach & Jean Sciare & Hang Su & Ulrich Pöschl, 2020. "Model Calculations of Aerosol Transmission and Infection Risk of COVID-19 in Indoor Environments," IJERPH, MDPI, vol. 17(21), pages 1-18, November.
    16. Ledyz Cuesta-Herrera & Luis Pastenes & Ariel D. Arencibia & Fernando Córdova-Lepe & Cristhian Montoya, 2024. "Dynamics of Activation and Regulation of the Immune Response to Attack by Viral Pathogens Using Mathematical Modeling," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    17. Marziah Hashimi & T. Andrew Sebrell & Jodi F. Hedges & Deann Snyder & Katrina N. Lyon & Stephanie D. Byrum & Samuel G. Mackintosh & Dan Crowley & Michelle D. Cherne & David Skwarchuk & Amanda Robison , 2023. "Antiviral responses in a Jamaican fruit bat intestinal organoid model of SARS-CoV-2 infection," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    18. Hanyu Li & Kazuki Kuga & Kazuhide Ito, 2022. "SARS-CoV-2 Dynamics in the Mucus Layer of the Human Upper Respiratory Tract Based on Host–Cell Dynamics," Sustainability, MDPI, vol. 14(7), pages 1-18, March.
    19. Antonella De Donno & Giambattista Lobreglio & Alessandra Panico & Tiziana Grassi & Francesco Bagordo & Maria Pia Bozzetti & Serafina Massari & Luisa Siculella & Fabrizio Damiano & Francesco Guerra & M, 2021. "IgM and IgG Profiles Reveal Peculiar Features of Humoral Immunity Response to SARS-CoV-2 Infection," IJERPH, MDPI, vol. 18(3), pages 1-15, February.
    20. Andrea Mancusi & Federico Capuano & Santa Girardi & Orlandina Di Maro & Elisabetta Suffredini & Denise Di Concilio & Lucia Vassallo & Maria Concetta Cuomo & Maria Tafuro & Daniel Signorelli & Andrea P, 2022. "Detection of SARS-CoV-2 RNA in Bivalve Mollusks by Droplet Digital RT-PCR (dd RT-PCR)," IJERPH, MDPI, vol. 19(2), pages 1-13, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010536. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.